Answer:
It will take 9 years for the population to double
Step-by-step explanation:
Exponential Growth
The natural growth of some magnitudes can be modeled by the equation:
[tex]P=P_o(1+r)^t[/tex]
Where P is the actual amount of the magnitude, Po is its initial amount, r is the growth rate and t is the time.
The population of a city grows at a rate of r=8% = 0.08 per year. We are required to find when (t) the population will double, or P=2Po.
Substituting in the equation:
[tex]2P_o=P_o(1+0.08)^t[/tex]
Simplifying:
[tex]2=(1.08)^t[/tex]
Taking logarithms:
[tex]\log 2=\log (1.08)^t[/tex]
Applying the exponent property of logs:
[tex]\log 2=t\log (1.08)[/tex]
Solving for t:
[tex]\displaystyle t=\frac{\log 2}{\log (1.08)}[/tex]
Calculating:
[tex]t\approx 9[/tex]
It will take 9 years for the population to double
Y = [ ? ]
PLEASE HELP
Answer:
120
Step-by-step explanation:
First, you want to find the third angle
to do that you 180-33+87=60
x=60
since x and y are on a straight line, to find y would be 180-x
180-60=120
y=120
What is the value of x in the equation 6(x +11)= -300?
Answer:
-61
Step-by-step explanation:
We use the distributive property to distribute 6 to both x and 11. This gives 6x+66=-300. Subtracting both sides by 66 gives 6x=-366. Dividing both sides gives x=-61.
Archie Baines
Arthur is organising his collection
of DVDs. He has 56 altogether.
The ratio of comedy films to
action to horror is 2 : 7:5
Step-by-step explanation:
x - is the amount of DVDs
so 2x + 5x + 7x = 56
14x = 56
x = 4
so comedy is 2x4 = 8; action 7x4 = 28 and horror is 5x4 = 20 DVDs
pls help me figure this out!!! quick!!
Answer:
35 degrees
Step-by-step explanation:
I think that's a right angle? If so, right angles always are 90 degrees, and 90 - 55 = 35.
Rent-A-Car rents compact cars for a fixed amount per day plus a fixed amount of each mile driven. Ben rented a car for 6 days, drove it 550 miles, and spent $337. Lisa rented the same car for 3 days, drove it 350 miles, and spent $185. What is the charge per day and per mile to rent that car?
Answer:
$36 per day plus $0.22 per mile
Step-by-step explanation:
For Ben,
Total miles driven = 550 miles
Number of days = 6 days
Total cost = $337
For Lisa
Total miles driven = 350 miles
Number of days = 3 days
Total cost = $185
Solving Simultaneously;
6d + 550m = 337
3d + 350 m = 185
Multiply equation 2 by 2 we have
6d + 550m = 337 ----1
6d + 700m = 370------2
So;
Subtracting equation 1 from equation 2
150m = 33
m = 33/150
m = $0.22
Substitute m=0.22 into equation 1
6d + 550(0.22) = 337
6d + 121 = 337
6d = 337 - 121
6d = 216
d = 216/6
d = $36
Hence the charge is $36 per day plus $0.22 per mile
Just need the explain your answer part. Can anyone help seventh grade math please DESPRATE
9514 1404 393
Answer:
140, 35, 260/35, 7.43, 8
Step-by-step explanation:
The last section is just a summary of the preceding sections, a short description of the problem and how you worked it.
She sells the jackets for 140% of $25, or $35. 260/35 = 7.43 She can only sell a whole number of jackets, so she needs to sell 8.
if csc Ф = 4/3, what is the value of sin Ф
Answer:
sinθ = [tex]\frac{3}{4}[/tex]
Step-by-step explanation:
Using the trigonometric identity
sin x = [tex]\frac{1}{cscx}[/tex] , then
sin
θ = [tex]\frac{1}{\frac{4}{3} }[/tex] = [tex]\frac{3}{4}[/tex]
-28-4p=-4(p+7) please answer
How long will it take a plane to fly 183 miles at 122 miles per hour
Answer:
Total time = 1.5 hours
Step-by-step explanation:
Given:
Total distance = 183 miles
Speed = 122 miles per hour
Find:
Total time
Computation:
Total time = Total distance / Speed
Total time = 183 / 122
Total time = 1.5 hours
All tickets to a play have the same cost. A group bought 6 tickets and paid a total of $99. Write a multiplication equation that can be used to determine cost c in dollars for each ticket.
Unit rate is the quantity of an amount of something at a rate of one of another quantity.
The multiplication equation to determine the cost C in dollars of each ticket is C = 99 x 1/6.
The cost of each ticket is $16.5.
What is a unit rate?It is the quantity of an amount of something at a rate of one of another quantity.
Example:
6 miles in 2 hours
0ne hour will be 3 miles.
We have,
6 tickets = $99
Divide both sides by 6.
1 ticket = 99/6
1 ticket = $16.5
The multiplication equation to determine the cost C in dollars of each ticket:
$C = 99 x 1/6
Thus,
The multiplication equation to determine the cost C in dollars of each ticket is C = 99 x 1/6.
The cost of each ticket is $16.5.
Learn more about unit rates here:
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Jennifer spends 1/4 of the day at school then 3/4 with her friends how much time does she do in a day
if a person walks 1/2 mile in 1/4 hour, how far does that person walk in 1 3/4 hours at that rate?
Answer:
3 1/2 miles
Step-by-step explanation:
We can use a ratio to solve
1/2 mile x miles
----------------= ---------------
1/4 hour 1 3/4 hours
Changing to improper fractions
1/2 mile x miles
----------------= ---------------
1/4 hour 7/4 hours
Using cross products
1/2 * 7/4 = 1/4x
7/8 = 1/4x
Multiply each side by 4
7/2 = x
Changing back to a mixed number
3 1/2 =x
Audrey wants to ride her bicycle 44 miles this week. She has already ridden 12 miles. If she rides for 5 more days, write and solve an equation which can be used to determine x, the average number of miles she would have to ride each day to meet
her goal.
Answer:
4
Step-by-step explanation:
10.187 electric poles were fixed along a road at a regular interval of 20m. What was the total
distance fixed with the poles in km?
Answer:
203.74
Step-by-step explanation:
10.187x20=203.74m
203.74 = 0.20374 kilometres
I need help thank you.
Answer:
x ≤ 1
Step-by-step explanation:
The graph goes in the left direction, meaning the inequality needs to be less than.
The point is at the point positive 1 and has a shaded dot, meaning the inequality needs to be less than or equal to 1.
Answer:
B
Step-by-step explanation:
x ≤ 1
As thee circle at 1 is filled,you have to include 1 also
Which point (x,y) satisfies the given system of inequalities?
A. (3,-1)
B.(1,-6)
C. (-3,-1)
D. (-1,-6)
The answer is C: (-3,-1)
To test if points satisfy an equation, all you need to do is test the numbers in both of the equations it provides you
Here is proof the answer is C :
y > x - 2
(lets plug in point C)
-1 > -3 - 2
solve
-1 > -5 ?
Yes this statement is true- onto the next inequalitity!
y > 2x + 2
-1 > 2(-3) + 2
solve
-1 > -6 + 2
-1 > -4 ?
Yes, this inequality is true too!
Know we know answer c (-3,-1) is the right answer!
Ooooooooommkkekekeekkkekekeeekkeek leplelelellle
Step-by-step explanation:
Ooooooooommkkekekeekkkekekeeekkeek leplelelellle to u too
Need help!! Please!! Offering 20 points!
Answer:i
Step-by-step explanation:
The number 7.2 can be classified as:
a. real and rational
b. real and irrational
c. real and integer
d. real and whole
there are 88 girls and 96 boys in the sixth-grade what is the rate of girls to boys
A- 88 girls for every 96 boys
B- i girl for every 1.09 boys
C- 44 girls for every 48 boys
D- 11 girls for every 12 boys
Answer:
There are 11 Girls for every 12 Boys in the sixth-grade class
Step-by-step explanation:
For this problem, you want to take the original rate which is 88 girls / 96 boys.
Once you have that number, you want to divide both sides by 8.
88/96 = 11/12
The correct option is D. 11 girls for every 12 boys.
We need to determine the ratio of the number of girls to the number of boys.
Given:
Number of girls = 88
Number of boys = 96
The ratio of girls to boys can be represented as "girls : boys."
To simplify the ratio, we can divide both the number of girls and the number of boys by their greatest common divisor (GCD). In this case, the GCD of 88 and 96 is 8.
Dividing both numbers by 8, we get:
Number of girls (after dividing) = 88 ÷ 8 = 11
Number of boys (after dividing) = 96 ÷ 8 = 12
So, the simplified ratio of girls to boys is 11 : 12.
Now, let's check which option matches the simplified ratio:
A. 88 girls for every 96 boys (Does not match)
B. 1 girl for every 1.09 boys (Does not match)
C. 44 girls for every 48 boys (Does not match)
D. 11 girls for every 12 boys (Matches)
The correct option is D. 11 girls for every 12 boys.
Learn more about Ratios here:
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An international company has 21,900 employees in one country. If this represents 27.2% of the company's employees, how many employees does it have in total?
Round your answer to the nearest whole number.
Answer:
Step-by-step explanation:
21,900 / 0.272 = 80,514.7
Annual Rainfall of Cities
How many intervals could represent an
annual rainfall of 30 in -36 in?
A) 2
B)4
C)3
D) 5
Annual Rainfall (in.)
OA
OB
Oc
Answer:
B: 4
Step-by-step explanation:
The graph shows that there is 4 units between the numbers 30-36.
Hope this helps!
Evaluate −6 − (−2). (1 point)
A.−4
B.−8
C.4
D.12
Answer:
A. -4
Step-by-step explanation:
−6 − (−2) = -6 + 2
= -4
Hope this helped :)
I need help for the 5th time
Answer:
3.2t - 2.4
Step-by-step explanation:
Given
- 3.6 - 1.9t + 1.2 + 5.1t ← collect like terms
= (- 1.9t + 5.1t) + (- 3.6 + 1.2)
= 3.2t + (- 2.4)
= 3.2t - 2.4
write the fraction 32/40 in simplest form
Answer:
4/5
Step-by-step explanation:
32/8=4
40/8=5
4/5
Somebody pls help me!!!
=====================================================
Explanation:
The similar red marks on the angles tell us those angles are congruent. So they are the same measure.
The sides opposite those congruent angles are the same length. This means AC = BC. This triangle is isosceles.
--------------
Solve for x
AC = BC
5x-8 = 2x+7 .... substitution
5x-8-2x = 7 ... subtract 2x from both sides
5x-2x = 7+8 ..... add 8 to both sides
3x = 15
x = 15/3 ... divide both sides by 3
x = 5
---------------
Use that x value to compute each side length
AB = 3x+11 = 3*5+11 = 15+11 = 26
BC = 2x+7 = 2*5+7 = 10+7 = 17
CA = 5x-8 = 5*5-8 = 25-8 = 17
Note how BC and CA are the same length (17 units). This helps confirm we have the right x value.
----------------
The last step is to add up all the side lengths to get the perimeter
perimeter of triangle = sum of all the sides
perimeter of triangle = side1 + side2 + side3
perimeter of triangle ABC = AB + BC + CA
perimeter of triangle ABC = 26 + 17 + 17
perimeter of triangle ABC = 60 units
Answer:
Step-by-step explanation:
Remark
The sides opposite the 2 base angles are equal. That gives you x. Then all you have to do is substitute in the 3 binomials.
Equation
5x - 8 = 2x + 7 Add 8 to both sides
Solution
5x - 8 + 8 = 2x + 7 + 8 Combine
5x = 2x + 15 Subtract 2x from both sides
5x-2x = 2x-2x + 15 Combine
3x = 15 Divide by 3
x = 5
Side length
5x - 8 = 5*5 - 8 = 25 - 8
5x - 8 = 17
3x + 11 = 3*5 + 11 = 15 + 11 = 26
Perimeter
17
17
26 Add
Perimeter = 60
Which is the formula for finding the sum of the interior angles of a polygon?
A. 180° (n – 1), where n is the number of sides
B. 90° (n – 2), where n is the number of sides
C. 90° (n – 1), where n is the number of sides
D. 180° (n – 2), where n is the number of sides
Answer:
The sum of the interior angles in a regular polygon is given by the formula 180(n – 2), where n is the number of sides in the polygon.
Step-by-step explanation:
Answer:
(n-2)x 180 degrees
Step-by-step explanation:
i have no idea what to do (dont mind the extra woork ik its wrong)
Answer:
A) Scale factor from A to B is 2
B) Length of left side is 3 and length of right side is 5.
Step-by-step explanation:
A) Length of the top side is 2.5 in A and is 5 in polygon B. 5/2.5 = 2, therefore scale factor is 2.
B) Because the scale factor is 2, each of the sides double while the angles stay the same. Therefore, the length of the side on the left is 3 and length of the side on the right is 5.
1.5 x 2 = 3
2.5 x 2 = 5
Part (a)
Divide the upper horizontal lengths of the two figures:
5/2.5 = 2
The scale factor is 2. This means figure B has side lengths twice as long compared to figure A.
Answer: Scale factor = 2=======================================================
Part (b)
The missing side length seems to be the diagonal side of figure B. I'm not sure what's going on with the vertical side 89.4 as that should be 3 instead (since 1.5*2 = 3).
The diagonal side is 5 units long since we double 2.5 to get 5.
Answers:
vertical side = 3
diagonal side = 5
Which of the tables represents a function? (5 points)
Table A
Inputs
Output
3
1
3
4
2
3
Table B
Input
Output
2
7
5
6
2
9
Table C
Input
Output
1
5
7
2
7
3
Table D
Input
Output
3
4
1
5
8
5
Group of answer choices
Table C
Table D
Table A
Table B
Answer:
It's table D
Step-by-step explanation:
I just took the test.
Answer:
The answer is table D!
Step-by-step explanation:
Is the following fraction terminating or repeating? *
-3
__
7
Terminating
Repeating
Answer:
repeating -0.428571.....